diff --git a/src/header/map.rs b/src/header/map.rs
index 08a1b8bc..e16d6317 100644
--- a/src/header/map.rs
+++ b/src/header/map.rs
@@ -2368,7 +2368,11 @@ impl<'a, T> Iterator for Iter<'a, T> {
         let map = self.map;
         debug_assert!(map.entries.len() >= self.entry);
 
-        let lower = map.entries.len() - self.entry;
+        let mut lower = map.entries.len() - self.entry;
+        if self.cursor.is_none() {
+            // The current entry is exhausted. Saturate for an empty map.
+            lower = lower.saturating_sub(1);
+        }
         // We could pessimistically guess at the upper bound, saying
         // that its lower + map.extra_values.len(). That could be
         // way over though, such as if we're near the end, and have
@@ -2453,7 +2457,11 @@ impl<'a, T> Iterator for IterMut<'a, T> {
     fn size_hint(&self) -> (usize, Option<usize>) {
         debug_assert!(self.entries_len >= self.entry);
 
-        let lower = self.entries_len - self.entry;
+        let mut lower = self.entries_len - self.entry;
+        if self.cursor.is_none() {
+            // The current entry is exhausted. Saturate for an empty map.
+            lower = lower.saturating_sub(1);
+        }
         // We could pessimistically guess at the upper bound, saying
         // that its lower + map.extra_values.len(). That could be
         // way over though, such as if we're near the end, and have
diff --git a/tests/header_map.rs b/tests/header_map.rs
index f6210135..67505c2e 100644
--- a/tests/header_map.rs
+++ b/tests/header_map.rs
@@ -690,6 +690,37 @@ fn ensure_miri_sharedreadonly_not_violated() {
     let _foo = &headers.iter().next();
 }
 
+#[test]
+fn iter_size_hint() {
+    fn check(mut iter: impl Iterator, len: usize) {
+        for remaining in (0..=len).rev() {
+            let (lower, upper) = iter.size_hint();
+            assert!(lower <= remaining, "lower {lower} > remaining {remaining}");
+            if let Some(upper) = upper {
+                assert!(upper >= remaining);
+            }
+            assert_eq!(iter.next().is_some(), remaining > 0);
+        }
+        assert_eq!(iter.size_hint().0, 0);
+        assert!(iter.next().is_none());
+    }
+
+    for counts in [vec![], vec![1], vec![3], vec![1, 1], vec![3, 1, 2]] {
+        let mut headers = HeaderMap::new();
+        for (i, count) in counts.into_iter().enumerate() {
+            let name = HeaderName::from_bytes(format!("header-{i}").as_bytes()).unwrap();
+            for _ in 0..count {
+                headers.append(name.clone(), HeaderValue::from_static("x"));
+            }
+        }
+        let len = headers.len();
+        check(headers.iter(), len);
+        check(headers.iter_mut(), len);
+        check(headers.values(), len);
+        check(headers.values_mut(), len);
+    }
+}
+
 #[test]
 fn ensure_miri_itermut_not_violated() {
     let mut headers = HeaderMap::<u32>::default();